Question

The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.7 years and a standard deviation of 0.6 years. He then randomly selects records on 48 laptops sold in the past and finds that the mean replacement time is 3.4 years.

Assuming that the laptop replacement times have a mean of 3.7 years and a standard deviation of 0.6 years, find the probability that 48 randomly selected laptops will have a mean replacement time of 3.4 years or less.
P(M < 3.4 years) =

Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Based on the result above, does it appear that the computer store has been given laptops of lower than average quality?

• No. The probability of obtaining this data is high enough to have been a chance occurrence.
• Yes. The probability of this data is unlikely to have occurred by chance alone.

Answer 1

Answer

Using normalcdf

setting lower = -99

upper =3.4

mean = 3.7

and sigma = 0.6/sqrt(48)

we get

P(xbar<3.4) = normalcdf(-99,3.4,3.7,0.6/sqrt(48))

= 0.0003

we can see that this probability is unusual because it is less than 0.05 cut off value

so, we can say that the probability of the given data is high enough to have been a chance occurrence

option A is correct